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|3x+4|=16

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| $3$ x+ $4$ |= $16$ $\newline$ ◻ $\newline$ Question Help: $\newline$ ◻ Video $\newline$ Submit Question

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Integer inequalities with absolute values

Full solution

Q. |

3

x+

4

|=

16

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Understand absolute value equation: Understand the absolute value equation. $\newline$ Absolute value equations have two possible solutions because the expression inside the absolute value can be either positive or negative to equal $16$ . $\newline$ $|3x + 4| = 16$
Set up separate equations: Set up two separate equations to solve. $3x + 4 = 16$ and $3x + 4 = -16$
Solve first equation: Solve the first equation $3x + 4 = 16$ . $\newline$ $3x = 16 - 4$ $\newline$ $3x = 12$ $\newline$ $x = \frac{12}{3}$ $\newline$ $x = 4$
Solve second equation: Solve the second equation $3x + 4 = -16$ . $3x = -16 - 4$ $3x = -20$ $x = \frac{-20}{3}$ $x = -6.67$

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